Valve switch modulation for reducing errors due oscillations of the inlet fluid of a pump system

ABSTRACT

Described is a method of reducing liquid composition errors in a low-pressure mixing pump system. Packets representing the switching intervals of each component of the desired fluid mixture are provided to an intake of the mixing pump system. For each packet, a switching time associated with at least one of the components in the packet is modulated. Modulated switching times are based on time offsets that are specifically selected according to the undesirable frequency characteristic of an intake response of the mixing pump system. The average of the volumes contributed by the packets thus modulated is equal to a component volume that achieves a desired proportion of the component in the output flow of the mixing pump system. Modulated switching times enable the reduction or elimination of composition error in the output flow of the mixing pump system.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the National Stage of International Application No.PCT/US2009/056434, filed Sep. 10, 2009 and designating the UnitedStates, which claims benefit of a priority to U. S. Provisional PatentApplication No. 61/096,480, filed Sep. 12, 2008. The contents of theseapplications are expressly incorporated herein by reference in itsentirety.

FIELD OF THE INVENTION

The invention relates generally to switching valves in liquid pumpsystems. More particularly, the invention relates to a method forreducing errors resulting from the intake fluid behavior of a gradientproportioning valve in a low pressure gradient pump system for liquidchromatography.

BACKGROUND OF THE INVENTION

A variety of applications exist in which the need to meter two or moreliquids in accurately controlled proportions is critical. One suchapplication is liquid chromatography wherein an analyte sample is passedin a flow of liquid solvent (the mobile phase) through a column packedwith particulate matter (the stationary phase). While passing throughthe column, the various components in the sample separate from oneanother by adsorbing and desorbing from the stationary phase atdifferent rates such that the individual components elute from thecolumn at different times. The separated components flow through adetector which responds to each component and provides information tothe user about the constituents of the sample.

To achieve more effective separations, high performance liquidchromatography (HPLC) systems often use mixtures of solvents as themobile phase. When this mixture is held constant, the system operates inan isocratic mode. More conventionally, the system operates in agradient mode whereby the components of the mixture are changed overtime.

As used herein, a packet means a sequential contribution of fluidcomponents provided to the pump intake. FIG. 1 graphically depicts anexample of two consecutive packets where each packet includescontributions from a first solvent A, then a second solvent B, then athird solvent C and finally a fourth solvent D. A slice as used hereinmeans the contribution of a single component to a packet. Thus thevolume of component A in each packet is the first slice for the packet,the volume of component B in each packet represents the second slice forthe packet, and so forth.

During gradient chromatography, metering and accuracy of the pump systemis dependent on the valves controlling the volume of fluid drawn intothe pump for each slice. Conventional metering techniques are based onan intake flow that accurately follows the commanded flow; however, theintake flow typically behaves like an underdamped system. FIG. 2 showsan example of the flow error due to the switching of a valve. Asillustrated, the flow error is a decaying sinusoid. The flow errors fora given system vary according to the gas solubility, viscosity, andcompliance of the solvents and other factors relating to hydraulicinertia. Subsequent switching of the valves typically results in errorsin the relative proportions of the components unless the switchingoccurs at a zero error crossing. Moreover, each additional switchingevent similarly results in a new intake flow disturbance andcorresponding flow error that can adversely affect the desiredproportions of components.

Thus liquid chromatography performance being greatly dependent on thecompositional accuracy of the solvent mixture is typically limited byerrors due to the system intake response of the pump system andproportioning valve. The present invention addresses the need to reducethese errors.

SUMMARY OF THE INVENTION

The invention relates to a method for reducing composition error in theoutput flow of a low pressure mixing pump system due to the intakebehavior of the pump system. Actuation of the switching valves for oneor more of the components vary in time with respect to the initiation ofa packet. This modulation of the actuation times and the consequentialmodulation of corresponding component volumes are performed in a mannerthat preserves the average of the component volumes to achieve thedesired proportions in the output flow of the pump system. Themodulation pattern is specifically selected according to frequencycharacteristics of the intake response of the pump system to reduce orcancel related errors.

In one aspect, the invention features a method of reducing compositionerror in the output flow of a mixing pump system. For each packet in agroup of packets provided to an intake of the mixing pump system, aswitching time of at least one of the components in the packet ismodulated. The modulated switching times are determined from switchingtime offsets. The switching time offsets are determined in response to afrequency characteristic of an intake response of the mixing pumpsystem. An average of a component volume for each component is equal toa component volume predetermined to achieve a proportion of thatcomponent in the output flow.

In another aspect, the invention features a method of reducingcomposition error in the output flow of a mixing pump system. A firstvalve is actuated during a first packet to provide a first volume of afirst component to an intake of the mixing pump system. A second valveis actuated during the first packet to provide a first volume of thesecond component to the intake of the mixing pump system. The firstvalve is actuated for at least one subsequent packet to provide anadditional volume of the first component to the intake of the mixingpump system. The second valve is actuated for at least one subsequentpacket to provide an additional volume of the second component to theintake of the mixing pump system. At least two of the volumes of thefirst component differ and at least two of the volumes of the secondcomponent differ. The average of the volumes of the first component andthe average of the volumes of the second component volume equalrespective component volumes predetermined to achieve a proportion ofthe respective component in the output flow.

In yet another aspect, the invention features a mixing pump systemhaving reduced composition error in an output flow. The mixing pumpsystem includes a gradient proportioning valve, a pump and a systemcontroller. The gradient proportioning valve has an outlet port andmultiple fluid switching valves each adapted for providing a componentto an intake flow. The pump has an inlet port coupled to the outlet portof the gradient proportioning valve. The system controller is incommunication with the gradient proportioning valve and the pump, andprovides a signal to the gradient proportioning valve to actuate thefluid switching valves at modulated switching times. The modulatedswitching times are determined from switching time offsets. Theswitching time offsets are determined in response to a frequencycharacteristic of an intake response of the mixing pump system. Anaverage of a component volume for each of the components equals acomponent volume predetermined to achieve a proportion of the respectivecomponent in the output flow.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and further advantages of this invention may be betterunderstood by referring to the following description in conjunction withthe accompanying drawings, in which like numerals indicate likestructural elements and features in the various figures. For clarity,not every element may be labeled in every figure. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

FIG. 1 is an illustration of an example of two consecutive packetscomposed of slices.

FIG. 2 graphically illustrates flow error resulting from the switchingof a valve.

FIG. 3 is a block diagram of a liquid chromatography system that can beused to practice an embodiment of the method of the invention.

FIG. 4 illustrates the reduction of flow error in comparison to the flowerror of FIG. 2 resulting from switching time offset modulationaccording to an embodiment of the invention.

FIG. 5 graphically illustrates examples of a binary gradient forunmodulated switching times and a binary gradient achieved usingmodulated switching times according to an embodiment of the method ofthe invention.

FIGS. 6A and 6B graphically illustrate a six-point modulation scheme andthe corresponding frequency response according to an embodiment of theinvention.

FIG. 7 is a timeline depicting an embodiment of the method of theinvention using a two-point modulation scheme to control the switchingof four solvents.

FIGS. 8A to 8H illustrate the application of an embodiment of the methodof the invention according to a first rule for different values ofpackets per pump stroke and slices per packet.

FIG. 9 illustrates the application of an embodiment of the method of theinvention according to a second rule for two packets per pump stroke andthree slices per packet.

FIG. 10A and FIG. 10B graphically illustrate an example of a timelinefor switching events based on switching time modulation and a modifiedtimeline based on a collapsed vector of switching time offset valuesaccording to an embodiment of the method of the invention.

DETAILED DESCRIPTION

In brief overview, the invention relates to a method for reducingcomposition error in the output flow of a low pressure mixing pumpsystem due to the intake behavior of the pump system. Actuation of theswitching valves for one or more of the components vary in time withrespect to the initiation of a packet. This modulation of the actuationtimes and the consequential modulation of corresponding componentvolumes are performed in a manner that preserves the average of thecomponent volumes necessary to achieve the desired proportions. Themodulation pattern is specifically selected according to frequencycharacteristics of the intake response of the pump system to reduce orcancel related errors. The method produces predictable results that donot vary in time.

In the following description, the switching of proportioning valves isgenerally specified with respect to time; however, in preferredembodiments switching is referenced to the volume domain according tocomponent volume. For example, switching events may be indexed to pumpstroke displacement or stepper motor position so that variations from aconstant inlet flow rate can be accommodated.

FIG. 3 is a block diagram of a liquid chromatography system 10 that canbe used to practice the method of the invention. The system 10 includesa system controller 14 (e.g., microprocessor) in communication with auser interface device 18 for receiving input parameters and displayingsystem information. The system controller 14 communicates with a valvedrive module 22 for operating a gradient proportioning valve (GPV) 26and a motor drive module 30 for operating one or more stepper motors fora pump system 34. The pump system 34 can include complementary pumpheads that are operated in opposite phase as is known in the art. Thegradient proportioning valve 26 includes a plurality of fluid switchingvalves which are in turn connected by tubing to respective componentreservoirs 38A, 38B, 38C, 38D that hold the components (solvents) to becombined. The fluid switching valves of the gradient proportioning valve26 are coupled through a common outlet port which in turn is connectedto the inlet port of the pump system 34. The outlet port of the pumpsystem 34 delivers the mixture of solvents to a chromatographic column42, typically at much higher pressures.

During operation of the liquid chromatography system, the switchingvalves of the gradient proportioning valve 26 are opened sequentially sothat the pump system 34 draws liquid from each of the reservoirs 38. Theproportions of solvents present in the liquid mixture delivered by thepump system 34 depend on the relative actuation time of each of theswitching valves in relation to the inlet velocity profile during theintake cycle.

As described above, the initiation of intake for a pump typicallyresults in the start of an intake response as shown in FIG. 2 where anerror occurs in the desired intake flow rate. According to the method ofthe invention, switching times (i.e., the times at which the switchingvalves are actuated) are carefully determined so that the volumecontributions for each slice of a given solvent average to a desiredvalue. These switching times are offset in time from switching timesused in a conventional pump system in which the error in the intake flowrate due to the intake response is ignored or left uncompensated.

In one embodiment of the method, if a dominant frequency appears in theintake response as depicted in FIG. 2, a two-point offset modulation ofthe switching times is used to target the dominant frequency and therebysignificantly reduce the error. Instead of operating the switching valveat the proportioned time after each packet initiation time, as with aconventional pump system, the switching valve is actuated early byone-quarter of the period of the sinusoid and on the newt packet, theswitching valve is actuated late by one-quarter of the period of thesinusoid. The earlier switching time T₁ is used for the first slice ofthe solvent and the later switching time T₂ is used for the slice of thesolvent in the next packet. Switching times T₁ and T₂ are alternated forsubsequent packets. Thus the volume of the solvent introduced in theslice starting at the earlier switching time T₁ is slightly greater thanthe amount necessary to maintain the desired proportion of solvents;however, the volume of the solvent introduced in the slice for the nextpacket starting at the later switching time T₂ is slightly less than theproper amount. Consequently, the average volume of the solvent remainsunchanged from that of an unmodulated pump system with no flow error. Ina complementary manner, the volume of a solvent in the slice thatimmediately precedes the modulated switching events is first less thanand then subsequently greater than the desired volume for that solventsuch that its average volume is also the same as the volume of thatsolvent for a slice in an unmodulated pump system with no flow error.For embodiments in which the offset modulation uses three or moremodulation points, there is no requirement for complimentary offsettimes as in the two-point offset modulation scheme; however, the averagecontributions of the solvents after utilizing all the modulation pointsare the same as the volumes of the solvents for respective slices in anunmodulated pump system without flow error.

Although the times T₁ and T₂ are shown in the example based on FIG. 2 tocorrespond to a maximum flow error and a subsequent minimum flow error,in other embodiments the switching times occur at other positions(times) in the intake response, although the difference in the switchingtimes T₁ and T₂ remains the same. FIG. 4 illustrates how this errorvaries in time for other positions of T₁ and T₂ relative to the intakeresponse. Due to the decaying nature of the sinusoidal intake response,the error is generally not completely eliminated; however, the error isgenerally much less than the error that occurs in a system withoutswitching time modulation. In effect, the determination of the switchingtimes according to the invention is based on digital filtering. For atwo-point modulation scheme the digital filter targets the dominantfrequency of the sinusoidal intake response. In this case, thedifference between times T₁ and T₂ is half the period of the sinusoidalintake response.

In general, a more complex pattern of switching to accommodate a rangeof frequencies present in an intake response is preferred. The switchingtime offsets correspond to a digital filter implementation where theoffsets are selected to achieve the desired filter frequencycharacteristic. Using more switching time offsets generally enablesbetter filter frequency control; however, more switching time offsetsrequires more time to achieve the proper volume averages and thereforecan make mixing more difficult. The sum of the switching time offsetsare zero so that the average of the switching times matches theswitching time in an unmodulated system with no flow error.Consequently, the desired solvent proportions are achieved. In effect,the method of the invention is based on a tradeoff: compositional noiseis introduced to the pump system by inducing offsets in the switchingtimes; however, the accuracy of the pump system as measured according tocomponent volumes is improved.

FIG. 5 shows an example of a linear gradient for a two solvent liquidphase (i.e., a binary gradient). The line 50 indicates the gradientachieved using a gradient proportioning valve with modulated switchingtimes according to the method of the invention. The line 54 indicatesthe gradient achieved using a gradient proportioning valve with fixed(unmodulated) switching times. Although high frequency deviations from alinear gradient are observable for the modulated gradient 50, thesedeviations are small with respect to deviation from a linear gradientfor the unmodulated system.

The desired frequency characteristic of the digital filter is determinedby measurement for a range of solvents of interest and the switchingtimes are selected based on the determined frequency characteristic.FIG. 6A shows an example of a six-point modulation scheme and FIG. 6Bshows the corresponding frequency response. Switching is performed insequence at the times T₁, T₂, T₃, T₄, T₅ and T₆. The unmodulatedswitching time T₀ for a conventional pump system is shown for comparisonand is the same as the average for the modulated switching times. TimesT₁, T₃ and T₅ represent delayed switching relative to the averageswitching time T₀ and times T₂, T₄ and T₆ are advanced relative to theaverage switching time T₀.

The switching time offsets shown in FIG. 6A are symmetricallydistributed about the average switching time T₀ so that the number ofadvanced switching events equals the number of delayed switching events.In other embodiments the number of switching time offsets can be odd sothat there is no symmetry about the average switching time T₀, althoughthe average switching time is maintained at T₀. Preferably, theswitching time offsets are implemented in an order such that the averageof any two switching time offsets is approximately zero to better shapethe noise introduced in the modulation process.

FIG. 7 is a timeline depiction for an embodiment of the method of theinvention using a two-point modulation scheme. As illustrated, themethod is used to control the switching of four solvents A, B, C and Dper packet with one packet occurring for each pump stroke. Actuation ofeach switch to provide the corresponding solvent results in an intakeresponse in the form of a decaying sinusoid as described above. On afirst pump stroke, actuation of switch 1 for solvent B occurs at timeT_(B1) and results in the intake response labeled Switch 1—Packet 1. Onthe next pump stroke, actuation of switch 1 for solvent B occurs at timeT_(B2) and results in the intake response labeled Switch 1—Packet 2. Thetwo offset intake responses resulting from the modulation of switch 1for solvent B permits switch 2 for solvent C to be unmodulated. Morespecifically, a first actuation of switch 2 at time T_(C) occurs at arelative low point in the Switch 1—Packet 1 intake response of solvent Band the next actuation of switch 2 during the next packet at time T_(C)occurs at a relative high point in the Switch 1—Packet 2 intakeresponse. Effectively, the actuation time of switch 2 is modulated withrespect to the intake response of solvent B in an alternating mannerabout an average value without actually changing the modulation timeT_(C) relative to the intake initiation time T_(A). Thus the variationof the volume for each slice of solvent B is due only to the modulationof switch 1. As switch 2 has no offset modulation, the actuation timeT_(D) of switch 3 is modulated to prevent the intake response forsolvent D from always starting at the same position along the intakeresponse of solvent C. As shown, switch 3 actuates first at a timeT_(D1) and then during the next packet at a time T_(D2) with furtherswitch actuations for subsequent packets occurring in an alternatingfashion.

It should be recognized that the switching time modulation describedwith reference to FIG. 7 can be extended in a more general sense to anynumber of solvents. In particular, switching time modulation is appliedto the switches providing “even solvents” (e.g., solvent B and solventD) while no modulation of the switching times is necessary for “oddsolvents” (e.g., solvent A and solvent C).

The method of the invention can be described more generally as follows.The switching time offsets d are defined by a vector having n elementseach indicating a switching time offset value (d₁, d₂, d₃, . . . ,d_(n)). m is a variable representing the index of the elements of thevector. Once all switching time offsets values d are used (i.e., m>n),the values d are used again in order starting with d₁, (i.e., m=(m modn)+1).

The method is applied according to either of two rules where theparticular rule selected is determined according to the number ofpackets per pump stroke and the number of slices per packet. The firstrule is applied if the number of packets per pump stroke does not exceedone or if the number of slices per packet is an even number. Accordingto the first rule, modulation is performed for the first switching eventand every other switching event in a pump stroke. The occurrence of anew pump stroke resets the counting of the switching events for a pumpstroke. For each new packet, the next value in sequential order in theswitching time offset vector is used.

FIG. 8A to FIG. 8H illustrate the application of the first rule fordifferent values of packets per pump stroke (PpS) and slices per packet(SpP). Dashed vertical lines are used to show the initiation of a pumpstroke. Hashed areas depicted under the switching time offset “d_(n)”are used to indicate the increase and decrease in time and volume forthe adjacent slices.

FIG. 8A illustrates one packet per pump stroke and two slices perpacket, and FIG. 8B illustrates two packets per pump stroke and twoslices per packet. FIG. 8C illustrates one-half packet per pump strokeand two slices per packet. FIGS. 8D, 8E and 8F illustrate one, two andon-half packets per pump stroke, respectively, for four slices perpacket. FIGS. 8G and 8H illustrate one and one-half packets per pumpstroke, respectively, for three slices per packet. Either two or fourelements are included in the switching time offset vector for theillustrated cases.

The second rule is applied when the number of packets per pump stroke isgreater than one and the number of slices per packet is an odd number.Similar to the first rule, modulation is performed for the firstswitching event and every other switching event in a pump stroke. Theswitching time offsets d are selected as d_((st+dsw)) from the switchingtime offset vector where St is the pump stroke number and dsw is themodulated switch number. The value of dsw resets to zero at the start ofa pump stroke because the intake response in one intake of the dual headpump system does not have an effect on the following intake stroke atthe other intake. An alternative technique is to apply a singleswitching time offset for each pump stroke; however, this alternative isnot preferred as it generates longer term noise than is necessary toachieve the desired error reduction.

FIG. 9 is an example application of the second rule for a case in whichthere are two packets per pump stroke and three slices per packet. Thefirst switching occurrence between solvents B and C and the secondswitching occurrence between solvents A and B in a pump stroke areunmodulated because they are “even-numbered” switching events within thepump stroke. For the first and subsequent “odd-numbered” switchingoccurrences in a pump stroke the switching time offsets chosen from theswitching time offset vector are incremented by one relative to theswitching time offsets used in the previous stroke.

Table 1 summarizes how the switching time offsets are applied in a moregeneral sense. The number of switching time offsets that are used isdetermined by the number n of elements in the vector. When m increasesso that it exceeds n, m is reset and the switching time offsets areagain used in order of occurrence in the vector beginning with d₁.

TABLE 1 Stroke Number Modulated Switching Number (dsw) (st) 1 2 3 4 m 1d₁ d₂ d₃ d₄ d_(m) 2 d₂ d₃ d₄ d₅ d₁ + m 3 d₃ d₄ d₅ d₆ d₂ + m 4 d₄ d₅ d₆d₇ d₃ + m n d_(n) d_(n) + 1 d_(n) + 2 d_(n) + 3 d_(n) + m

Every switching event and the beginning and the end of pump strokes areoccurrences which generally are accounted for when implementing themethod of switching time modulation according to the invention. Inparticular, the minimum time for the actuation of a switch and theavailable time T_(AVAIL) measured from the unmodulated switching time tothe next event, such as the next switching time or the beginning of thenext stroke, can limit application of the method. To accommodate suchlimitations, one embodiment of the method includes scaling, or“collapsing,” the vector of switching time offset values.

To decide whether collapsing is to be performed, the available timeT_(AVAIL) about a switching time is determined. The value of a parameterK is given byK=T _(AVAIL)/max(abs(d))where the numerator is the maximum value determined from the absolutevalues of the switching time offset values in the vector. If K is equalto or greater than one, no collapsing is necessary as the available timeT_(AVAIL) accommodates all of the switching time offsets; however, if Kis less than one, all elements of the vector are scaled by K so that thewidth of the switching time modulation range is effectively collapsed.Scaling of the switching offset times ensures that all switching timeoffsets can be used within the available time T_(AVAIL).

FIG. 10A and FIG. 10B graphically illustrate an example of a timelinefor switching events based on switching time modulation and a modifiedtimeline based on a collapsed vector of switching time offset values. InFIG. 10A there are six different switching times t₁ to t₆ correspondingto six switching time offsets d₁ to d₆, respectively. The time T_(AVAIL)indicates the latest time in which a switching event is allowed tooccur. Times t₁ and t₃ occur after the expiration of available timetherefore the vector of switching time offset values is scaled by theconstant K as shown in FIG. 10B so that all possible modulated switchingtimes t′ are accommodated in the available time. The value of K isselected such that the full spread of possible switching times based onthe vector fits into the available time.

The frequency characteristic of the digital filtering performed with thecollapsed switching time offsets scales according to the value of K. Anexample of this effect can be seen by again referring to FIG. 5 wherethe modulation observed on the linear gradient 50 is significantlydecreased in the lowest and highest concentration regions.

In a preferred embodiment, the commanded switching times for thegradient proportioning valve are advanced (i.e., “time-shifted”) toensure that valve actuation occurs at the proper time to overcome valvedelay and thereby provide the desired volumes for the slices. As thepump works in the volume/motor position domain, the time shift isconverted to motor steps. To reduce complexity, a constant intakevelocity is assumed; therefore positional shift is equal to velocitymultiplied by time shift. This assumption yields error when the timeshifts occur on the acceleration and deceleration regions of the intakevelocity profile. This error is generally small therefore the constantintake velocity assumption is sufficient in most cases.

The above descriptions and embodiments are based on time and a constantpump velocity, therefore the volume variations for each slice due toswitching time offset modulation are averaged out. In another preferredembodiment, the switching time offsets are converted into position stepsof the pump motor. More specifically, the timing is mapped to steppermotor position to account for variation of the intake volume of the pumpin time so that a volumetric average is achieved instead of a switchingtime offset average. This mapping is important when switching timesoccur early or late in a pump stroke when the pump velocity isaccelerating or decelerating.

While the invention has been shown and described with reference tospecific embodiments, it should be understood by those skilled in theart that various changes in form and detail may be made therein withoutdeparting from the spirit and scope of the invention as recited in theaccompanying claims.

What is claimed is:
 1. A method of reducing composition error in theoutput flow of a mixing pump system, the method comprising, for eachpacket in a plurality of packets provided to an intake of the mixingpump system, modulating a switching time of at least one component in aplurality of components in the packet, the modulated switching timesbeing determined from a plurality of switching time offsets, wherein theswitching time offsets are determined in response to a frequencycharacteristic of an intake response of the mixing pump system andwherein an average of a component volume for each of the componentsequals a component volume predetermined to achieve a proportion of therespective component in the output flow.
 2. The method of claim 1wherein each modulated switching time is responsive to a commandedswitching time and wherein each commanded switching time occurs beforethe respective modulated switching time according to a respective valvedelay.
 3. The method of claim 1 wherein the switching time offsets arescaled to smaller values upon a determination that an availableswitching time is not of sufficient duration to include a modulatedswitching time according to at least one of the switching time offsets.4. The method of claim 1 wherein the modulated switching times andswitching time offsets are referenced to volume in an intake flow of themixing pump system.
 5. The method of claim 1 wherein the frequencycharacteristic of the intake response includes a dominant frequency andwherein the switching time offsets are an advance of one-quarter of aperiod corresponding to the dominant frequency and a delay ofone-quarter of a period corresponding to the dominant frequency.
 6. Themethod of claim 1 wherein a sum of the switching time offsets equalszero.
 7. The method of claim 1 wherein a number of advanced switchingtime offsets in the plurality of switching time offsets equals a numberof delayed switching time offsets in the plurality of switching timeoffsets.
 8. The method of claim 1 wherein a number of switching timeoffsets in the plurality of switching time offsets is odd and wherein anumber of advanced switching time offsets in the plurality of switchingtime offsets does not equal a number of delayed switching time offsetsin the plurality of switching time offsets.
 9. A mixing pump systemhaving reduced composition error in an output flow, comprising: agradient proportioning valve having an outlet port and a plurality offluid switching valves each adapted for providing a component to anintake flow; a pump having an inlet port coupled to the outlet port ofthe gradient proportioning valve; and a system controller incommunication with the gradient proportioning valve and the pump, thesystem controller providing a signal to the gradient proportioning valveto actuate the fluid switching valves at modulated switching times, themodulated switching times being determined from a plurality of switchingtime offsets, wherein the switching time offsets are determined inresponse to a frequency characteristic of an intake response of themixing pump system and wherein an average of a component volume for eachof the components equals a component volume predetermined to achieve aproportion of the respective component in the output flow.
 10. Themixing pump system of claim 9 wherein the signal provided by the systemcontroller to the gradient proportioning valve is referenced to volumein an intake flow of the mixing pump system.